An automated security gate hit my door, should I file a claim or get them to pay for the damages?

There was a parking spot near where the gate extends to and I parked too close. When the door opened, it bent the edge of my drivers side door. Should I call insurance or have a body shop give me a estimate? Will the company pay for the damages? The damages aren't too bad but I would like to get it fixed.

It's unlikely to company will pay for damages to your vehicle because, as you stated, you misjudged where the gate would open to. In terms of filing a claim with your insurance company, I recommend getting an estimate first to see how much the damage will cost. Especially because this type of claim would be considered a collision claim, which can impact your premium going forward. If the damages aren't too expensive, you're probably better off paying for it out of pocket.